In the Stranski-Krastanow growth of strained pseudomorphic films, material transport by surface diffusion plays a crucial role for the development of the three-dimensional island morphology. In an attempt to elucidate the atomistic aspects of this growth mode, we study diffusion of a single indium adatom on $(1\ifmmode\times\else\texttimes\fi{}3)$- and $(2\ifmmode\times\else\texttimes\fi{}3)$-reconstructed subcritical ${\mathrm{In}}_{2/3}{\mathrm{Ga}}_{1/3}\mathrm{As}(001)$ films using first-principles total energy calculations of the corresponding adiabatic potential-energy surfaces (PES). We find that In diffusion is anisotropic, and substantially enhanced compared to the conventional GaAs(001)-$c(4\ifmmode\times\else\texttimes\fi{}4)$ substrate. Special attention is also paid to the methodology of deriving the tracer diffusion coefficients of indium from knowledge of the PES, using the continuous-time random-walk formalism.
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